Divisibility Rules

Divisibility rules are used to know which number is exactly divisible by a particular number (s). Each number has a particular divisibility test. These rules are as follows: -
1. Divisibility test of number 2: A number is divisible by 2 if it has 0, 2, 4, 6 or 8 in its ones place. Example: 120, 552,374,1076,9998 all these are divisible by 2 as all these numbers contain 0,2,4,6,8 respectively in its unit (ones place).
2. Divisibility test of number 3: If the sum of the digits is a multiple of 3, then the number is divisible by 3. Example : 1263
1 + 2 + 6 + 3 = 12, 12 is divisible by 3 so the number 1,263 is divisible by 3.
3. Divisibility test of number 4: A number with three or more digits is divisible by 4 if the number formed by its last two digits i.e. ones and tens is divisible by 4. Example : 9284 :
Last two digits are 84 which are divisible by 4 so the number 9284 is divisible by 4.
4. Divisibility test of number 5: If a number has 0 or 5 in its ones place, then the number is divisible by 5. Example: 320 and 965 are divisible by 5 since the unit(ones digit) are 0 and 5 respectively so the given numbers are divisible by 5.
5. Divisibility test of number 6: A number that is divisible by both 2 and 3, then the given number is divisible by 6. Example : 342 : This number is divisible by 2 as unit(ones place) is 2 and the sum of the digits (3 + 4 + 2 = 9) is divisible by 3 so the 342 is divisible by both 2 and 3 so it is divisible by 6.
6. Divisibility test of number 8: A number with 4 or more digits is divisible by 8 if the number formed by last three digits is divisible by 8. Example : 45,216 Here last three digits 216 is divisible by 8 so 45,216 is divisible by 8.
7. Divisibility test of number 9: If the sum of the digits of a number is divisible by 9, then the number itself is divisible by 9. Example : 6561 :
6 + 5 + 6 + 1 = 18 , 18 is divisible by 9 so the number 6561 is divisible by 9.
8. Divisibility test of number 10: A number that has 0 in its ones place is divisible by 10. Example : 4,810 is divisible by 10 as unit digit(ones place) is zero.
9. Divisibility test of number 11: In order to check whether a number is divisible by 11 or not, find the difference between the sum of the digits at odd places (from the right) and the sum of the digits at even places (from the right) of the number. If the difference is either 0 or divisible by 11, then the number is divisible by 11. Example : 14,641
1 + 6 + 1 = 8
4 + 4 = 8
8 - 8 = 0 so the number 14,641 is divisible by 11.